Wave-Particle Duality

Diffraction and interference (Young’s double slit, single-slit patterns, diffraction gratings) only make sense if light is a wave — they depend on path differences and superposition, ideas with no meaning for a simple particle. Yet the photoelectric effect only makes sense if light arrives as discrete photons, each with energy $E=hf$, transferring all of that energy to one electron at once.

Neither model on its own explains everything light does. Depending on the experiment, light behaves as a wave or as a particle — never both properties measured in exactly the same way at once — and physicists simply accept both models are needed. This is $\text{wave-particle duality}$.

In 1924, Louis de Broglie proposed that this duality is not special to light — every moving particle with momentum $p$ has an associated wavelength, now called the $\text{de Broglie wavelength}$. Faster or heavier particles have more momentum and so a $\text{shorter}$ de Broglie wavelength; the effect only becomes noticeable for very light, fast-moving particles like electrons.

De Broglie’s hypothesis was confirmed by firing a beam of electrons through a thin film of polycrystalline graphite. If electrons were purely particles, you would expect them to pass straight through (or scatter randomly) and produce a diffuse blob on a detecting screen. Instead, a pattern of concentric bright and dark $\text{rings}$ is observed — a diffraction pattern, exactly like the pattern produced when X-rays (known waves) pass through the same kind of crystal structure.

The rings appear because the gaps between atomic planes in the graphite act like a diffraction grating for the electrons’ associated wave, with a spacing comparable to the electrons’ de Broglie wavelength. This experiment is the definitive, direct evidence that matter genuinely has wave properties, not merely a mathematical curiosity.

The resolution of any imaging system — the smallest detail it can distinguish — is fundamentally limited by the wavelength it uses; you cannot resolve detail much smaller than the wavelength involved. Visible light has a wavelength of a few hundred nanometres, which limits an optical microscope’s resolution to roughly that scale.

Electrons accelerated to a reasonable speed have a de Broglie wavelength thousands of times shorter than visible light, so an $\text{electron microscope}$, which focuses a beam of electrons using magnetic "lenses" instead of glass ones, can resolve details far smaller than any optical microscope — down to the scale of individual molecules.